Woods made his Broadway debut in Borstal Boy (1970) and his film debut a few years later in The Way We Were (1973). His other movies include The Onion Field (1979), Salvador (1986), for which he was nominated for an Oscar and won an Independent Spirit Award for Best Actor, Casino (1995), Ghosts of Mississippi (1996), for which he received a second Oscar nomination, and Contact (1997). He won Emmys for his work in The Promise (1986) and My Name Is Bill W. (1989).